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Using Cramer's Rule to find needed equations

  • Thread starter Final9mare
  • Start date
1. Homework Statement
I am finding the minimum coefficient μ between tires and road so that cars do not slide off. I have my equations for ƩFy and ƩFx and I know μ = [fs]/[/N]

So I would need to use cramer's rule on my equations to find fs and N.

But I am not sure how to use cramer's rule for my equations.


2. Homework Equations
ƩFx = Nsinθ -fscosθ = mv2/r
ƩFy = Ncosθ + fssinθ = mg

3. The Attempt at a Solution
I actually already have the answer but im not sure how to use cramer's to get to it.

fs = m(gsinθ-v2/r*cosθ)

N = m(v2/r*sinθ+gcosθ)
 

haruspex

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At a guess (which I should not be needing to do!) the car is negotiating a bend radius r, banked at angle theta (in the helpful direction).
ƩFx = Nsinθ -fscosθ = mv2/r
ƩFy = Ncosθ + fssinθ = mg
Sure about the sign of fs in those? Or is this calculating the minimum speed?
I actually already have the answer but im not sure how to use cramer's to get to it.
fs = m(gsinθ-v2/r*cosθ)
N = m(v2/r*sinθ+gcosθ)
You have two equations and two unknowns. You're accustomed to dealing with pairs of simultaneous equations, I trust.
 

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